Proportional Reasoning Section 2.2 Proportional Reasoning

Homework Pg 101 #19 - 31

If a proportion contains a variable, you can cross multiply to solve for the variable. When you set the cross products equal, you create a linear equation that you can solve by using the skills that you learned in Lesson 2-1.

Solving Proportions Solve each proportion. 14 c = 16 24 p 12.9 A. B. = 88 132 16 24 p 12.9 14 c 88 132 = = 206.4 = 24p Set cross products equal. 88c = 1848 206.4 24p 24 24 = 88c 1848 = Divide both sides. 88 88 8.6 = p c = 21

Solve each proportion. y 77 12 84 15 2.5 A. = B. = x 7 y 77 12 84 15 2.5 x 7 = = Set cross products equal. 924 = 84y 2.5x =105 924 84y 84 84 = = 2.5x 105 2.5 2.5 Divide both sides. 11 = y x = 42

Because percents can be expressed as ratios, you can use the proportion to solve percent problems. Percent is a ratio that means per hundred. For example: 30% = 0.30 = Remember! 30 100

Solving Percent Problems A poll taken one day before an election showed that 22.5% of voters planned to vote for a certain candidate. If 1800 voters participated in the poll, how many indicated that they planned to vote for that candidate?

At Clay High School, 434 students, or 35% of the students, play a sport. How many students does Clay High School have?

A rate is a ratio that involves two different units A rate is a ratio that involves two different units. You are familiar with many rates, such as miles per hour (mi/h), words per minute (wpm), or dollars per gallon of gasoline. Rates can be helpful in solving many problems.

Use a proportion to find the length of his stride in meters. Fitness Application Ryan ran 600 meters and counted 482 strides. How long is Ryan’s stride in inches? (Hint: 1 m ≈ 39.37 in.) Use a proportion to find the length of his stride in meters. 600 m 482 strides x m 1 stride = Write both ratios in the form . meters strides 600 = 482x Find the cross products. x ≈ 1.24 m

Luis ran 400 meters in 297 strides. Find his stride length in inches. Use a proportion to find the length of his stride in meters. 400 m 297 strides x m 1 stride = Write both ratios in the form . meters strides 400 = 297x Find the cross products. x ≈ 1.35 m

Nature Application The tree in front of Luka’s house casts a 6-foot shadow at the same time as the house casts a 22-fot shadow. If the tree is 9 feet tall, how tall is the house? Sketch the situation. The triangles formed by using the shadows are similar, so Luka can use a proportion to find h the height of the house. 9 ft 6 ft = 6 9 h 22 = Shadow of tree Height of tree Shadow of house Height of house h ft 22 ft 6h = 198 h = 33 The house is 33 feet high.